A Survey for New Members of Taurus from Stellar to Planetary Masses

TL;DR

This paper presents a comprehensive survey of Taurus star-forming region members, extending from stellar to planetary masses, using multi-wavelength data, spectroscopy, and Gaia astrometry, resulting in a nearly complete census including the faintest known planetary-mass objects.

Contribution

It provides the largest and most complete census of Taurus members across a wide mass range, including the discovery of the faintest planetary-mass objects and analysis of disk presence.

Findings

Nearly complete census for spectral types earlier than M6-M7.

Doubled the number of known members at ≥ M9.

Uncovered the faintest known planetary-mass member (~3-10 M_Jup).

Abstract

We present a large sample of new members of the Taurus star-forming region that extend from stellar to planetary masses. To identify candidate members at substellar masses, we have used color-magnitude diagrams and proper motions measured with several wide-field optical and infrared (IR) surveys. At stellar masses, we have considered the candidate members that were found in a recent analysis of high-precision astrometry from the Gaia mission. Using new and archival spectra, we have measured spectral types and assessed membership for these 161 candidates, 79 of which are classified as new members. Our updated census of Taurus now contains 519 known members. According to Gaia data, this census should be nearly complete for spectral types earlier than M6-M7 at A_J<1. For a large field encompassing ~72% of the known members, the census should be complete for K<15.7 at A_J<1.5, which corresponds to ~5-13 M_Jup for ages of 1-10 Myr based on theoretical evolutionary models. Our survey has doubled the number of known members at greater or equal to M9 and has uncovered the faintest known member in M_K, which should have a mass of ~3-10 M_Jup for ages of 1-10 Myr. We have used mid-IR photometry from the Spitzer Space Telescope and the Wide-field Infrared Survey Explorer to determine whether the new members exhibit excess emission that would indicate the presence of circumstellar disks. The updated disk fraction for Taurus is ~0.7 at less than or equal to M3.5 and ~0.4 at >M3.5.

Tables

Table 1. Table 1 Members of Taurus

Column Label	Description
2MASS	2MASS Point Source Catalog source name
UGCS	UKIDSS Galactic Clusters Survey source nameaaBased on coordinates from Data Release 10 of the UKIDSS Galactic Clusters Survey for stars with $K_s>10$ from 2MASS.
Gaia	Gaia DR2 source name
Name	Other source name
RAdeg	Right ascension (J2000)
DEdeg	Declination (J2000)
Ref-Pos	Reference for right ascension and declinationbbSources of the right ascension and declination are are the 2MASS Point Source Catalog, Gaia DR2, UKIDSS Data Release 10, and images from the Spitzer Space Telescope (Luhman et al., 2010).
SpType	Adopted spectral typeccSpectral types adopted by Luhman et al. (2017), Esplin & Luhman (2017), and Luhman (2018) for previously known members and types measured in this work for new members (Table 4).
GaiapmRA	Proper motion in right ascension from Gaia DR2
e_GaiapmRA	Error in GaiapmRA
GaiapmDec	Proper motion in declination from Gaia DR2
e_GaiapmDec	Error in GaiapmDec
plx	Parallax from Gaia DR2
e_plx	Error in plx
f_plx	Flag on parallaxdd* = Discrepant parallax relative to other members of Taurus, as noted in Luhman (2018) and the Appendix.
Gmag	$G$ magnitude from Gaia DR2
e_Gmag	Error in Gmag
GBPmag	$G_{\mathrm{BP}}$ magnitude from Gaia DR2
e_GBPmag	Error in GBPmag
GRPmag	$G_{\mathrm{RP}}$ magnitude from Gaia DR2
e_GRPmag	Error in GRPmag
RUWE	re-normalized unit weight error from Lindegren (2018)
Pop	Population from Luhman (2018)
IRpmRA	Proper motion in right ascension from 2MASS/WFCAM/IRAC
e_IRpmRA	Error in IRpmRA
IRpmDec	Proper motion in declination from 2MASS/WFCAM/IRAC
e_IRpmDec	Error in IRpmDec
Jmag	$J$ magnitude
e_Jmag	Error in Jmag
r_Jmag	Reference for Jmagee1 = 2MASS Point Source Catalog; 2 = UKIRT Hemisphere Survey; 3 = UKIDSS Data Release 10; 4 = our UKIRT photometry (Sec 3.1.3); 5 = WIRCam photometry.
Hmag	$H$ magnitude
e_Hmag	Error in Hmag
r_Hmag	Reference for Hmagee1 = 2MASS Point Source Catalog; 2 = UKIRT Hemisphere Survey; 3 = UKIDSS Data Release 10; 4 = our UKIRT photometry (Sec 3.1.3); 5 = WIRCam photometry.
Kmag	$K$ or $K_s$ magnitude
e_Kmag	Error in Kmag
r_Kmag	Reference for Kmagee1 = 2MASS Point Source Catalog; 2 = UKIRT Hemisphere Survey; 3 = UKIDSS Data Release 10; 4 = our UKIRT photometry (Sec 3.1.3); 5 = WIRCam photometry.
3.8mag	Spitzer [3.6] band magnitude
e_3.6mag	Error in 3.6mag
f_3.6mag	Flag on 3.6magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
4.5mag	Spitzer [4.5] band magnitude
e_4.5mag	Error in 4.5mag
f_4.5mag	Flag on 4.5magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
5.8mag	Spitzer [5.8] band magnitude
e_5.8mag	Error in 5.8mag
f_5.8mag	Flag on 5.8magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
8.0mag	Spitzer [8.0] band magnitude
e_8.0mag	Error in 8.0mag
f_8.0mag	Flag on 8.0magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
24mag	Spitzer [24] band magnitude
e_24mag	Error in 24mag
Ref-Spitz	Reference for Spitzer photometrygg1 = Luhman et al. (2010); 2 = Esplin et al. (2014); 3 = Esplin & Luhman (2017); 4 = this work.
f_24mag	Flag on 24magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
W1mag	WISE $W1$ band magnitude
e_W1mag	Error in W1mag
f_W1mag	Flag on W1magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
W2mag	WISE $W2$ band magnitude
e_W2mag	Error in W2mag
f_W2mag	Flag on W2magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
W3mag	WISE $W3$ band magnitude
e_W3mag	Error in W3mag
f_W3mag	Flag on W3magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
W4mag	WISE $W4$ band magnitude
e_W4mag	Error in W4mag
f_W4mag	Flag on W4magffnodet = non-detection; sat = saturated; out = outside of the camera’s field of view; bl = photometry may be affected by blending with a nearby star; bin = includes an unresolved binary companion; unres = too close to a brighter star to be detected; false = detection from WISE catalog appears false or unreliable based on visual inspection.
Exc4.5	Excess present in [4.5]?
Exc8.0	Excess present in [8.0]?
Exc24	Excess present in [24]?
ExcW2	Excess present in $W2$?
ExcW3	Excess present in $W3$?
ExcW4	Excess present in $W4$?
DiskType	Disk TypehhFrom Luhman et al. (2010), Esplin et al. (2014); Esplin & Luhman (2017), and this work.
Aj	Extinction in $J$
f_Aj	Method for estimating extinction in $J$ii$J-H$ and $J-K_s$ = derived from these colors assuming photospheric near-IR colors Luhman et al. (2010); CTTS = derived from $J-H$ and $H-K_s$ colors assuming intrinsic colors of classical T Tauri stars from from Meyer et al. (1997); opt spec = derived from an optical spectrum; IR spec = derived from an infrared spectrum; 1 = Briceño et al. (1998); 2 = Luhman (2000); 3 = Strom & Strom (1994); 4 = Beck (2007); 5 = White & Ghez (2001); 6 = DeWarf et al. (2003); 7 = Calvet et al. (2004).

Table 2. Table 2 Remaining Candidate Members of Taurus from Gaia

Gaia DR2 Source Name	$\alpha$ (J2000)aaGaia DR2.	$\delta$ (J2000)aaGaia DR2.	$G$aaGaia DR2.	RUWEbbLindegren (2018).	Notes
	($°$)	($°$)
152416436441091584	65.288914	27.843579	16.487	2.25	$0\stackrel{\prime \prime }{.}76$ from M5.25 member Gaia 152416436443721728
148400225409163776	69.936483	26.031919	20.392	1.50	$3\stackrel{\prime \prime }{.}11$ from M5 member ITG 15
154586322638884992	71.227352	27.296130	12.325	1.34	$1\stackrel{\prime \prime }{.}81$ from K1 member HD 283782
157816855305858176	71.458678	28.660584	6.724	2.37	HD 30111
157816859599833472	71.460272	28.659692	12.123	1.17	$5\stackrel{\prime \prime }{.}97$ from candidate HD 30111
3415706130945884416	78.115078	22.897051	14.303	9.74	$0\stackrel{\prime \prime }{.}64$ from M2.5 member Gaia 3415706130944329216

Table 3. Table 3 Observing Log

Telescope/Instrument	Disperser/Aperture	Wavelengths/Resolution	Targets
HET/LRS2	VPH grisms/$0\stackrel{\prime \prime }{.}6$ lenslets	0.65–1.05 $\mu$m/1800	2
IRTF/SpeX	prism/$0\stackrel{\prime \prime }{.}8$ slit	0.8–2.5 $\mu$m/150	41
Gemini North/GMOS	R400/$0\stackrel{\prime \prime }{.}5$ slit	0.6–1.0 $\mu$m/2000	21
Gemini North/GNIRS	31.7 l mm-1/$1″$ slit	0.9–2.5 $\mu$m/600	51
LAMOST	540 l mm-1/$3\stackrel{\prime \prime }{.}3$ fiber	0.37–0.9 $\mu$m/1500	31
MMT/Red Channel	270 l mm-1/$0\stackrel{\prime \prime }{.}75$ slit	0.58–0.92 $\mu$m/1000	34
MMT/Red Channel	1200 l mm-1/$0\stackrel{\prime \prime }{.}75$ slit	0.63–0.71 $\mu$m/3250	18
MMT/MMIRS	HK grism/$1\stackrel{\prime \prime }{.}2$ slit	1.25–2.34 $\mu$m/600	8

Table 4. Table 4 Spectroscopic Data for Candidate Members of Taurus

Source NameaaIdentifications from the 2MASS Point Source Catalog when available. Otherwise, they based on coordinates from data release 10 of the UKIDSS Galactic Clusters Survey.	Spectral	$W_{\lambda }$(Li)	Instrument	Date	Member?ccfootnotemark:
	Type	(Å)
2MASS J04002788+2031591	M6.5	$\cdots$	GNIRS	2017 Sep 2	N
2MASS J04005482+2117211	M8	$\cdots$	GNIRS	2017 Sep 27	N
2MASS J04005866+2014043	M4	0.2	SpeX,Red(1200)	2017 Oct 28,2018 Jan 2	N
UGCS J040132.09+260733.2	M9.5,M9.5	$\cdots$	SpeX,GNIRS	2017 Oct 30,2017 Sep 29	Y
2MASS J04053214+2733139	M4.75	$\cdots$	Red(270)	2017 Oct 22	N?

Table 5. Table 5 Disk Fraction for Taurus

Spectral Type	N(II)/N(II+III)
K6	24/33=${0.73}_{-0.09}^{+0.06}$
K6–M3.5	102/143=${0.71}_{-0.04}^{+0.03}$
M3.75–M5.75	64/148=$0.43\pm 0.04$
M6–M8	21/63=${0.33}_{-0.05}^{+0.06}$
$>$M8–M9.75	15/37=${0.41}_{-0.07}^{+0.08}$

Full text

1. Introduction

The Taurus cloud complex is one of the nearest star-forming regions ($d\sim 140$ pc, Galli et al., 2018, references therein) and has a relatively large stellar population ($N\sim 500$, Kenyon et al., 2008, this work), making it well-suited for studies of star formation that reach low stellar masses and have good statistics. In addition, Taurus has an unusually low stellar density compared to other nearby molecular clouds, so it can help constrain how the star formation process depends on environment. However, a complete census of Taurus is challenging given that its members are distributed across a large area of sky ($\sim 100$ deg2).

Surveys for members of Taurus have steadily improved in sensitivity and areal coverage over the last 30 years (Kraus et al., 2017; Luhman et al., 2017, references therein). We have recently sought to advance this work in Esplin & Luhman (2017) and Luhman (2018). In the first survey, we searched for members down to planetary masses ($<15$ $M_{\rm Jup}$) across a large fraction of Taurus using optical and infrared (IR) imaging from the Spitzer Space Telescope (Werner et al., 2004), the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS, Lawrence et al., 2007), Pan-STARRS1 (PS1, Kaiser et al., 2002, 2010), and the Wide-field Infrared Survey Explorer (WISE, Wright et al., 2010). Meanwhile, Luhman (2018) used high-precision astrometry and optical photometry from the second data release (DR2) of the Gaia mission (Perryman et al., 2001; de Bruijne, 2012; Gaia Collaboration et al., 2016b, 2018) to perform a thorough census of stellar members with low-to-moderate extinctions across the entire cloud complex.

We have continued the survey for low-mass brown dwarfs in Taurus from Esplin et al. (2018) by including new IR imaging from UKIRT and the Canada-France-Hawaii Telescope (CFHT). We also have obtained spectra of most of the candidate stellar members that were identified with Gaia by Luhman (2018). In this paper, we update the catalog of known members of Taurus from Luhman (2018) (Section 2), identify candidate members using photometry, proper motions, and parallaxes (Sections 3 and 4), and spectroscopically classify the candidates (Section 5). We assess the new members for evidence of circumstellar disks and estimate the disk fraction as a function of stellar mass among the known members (Section 6). We conclude by using our new census of Taurus to constrain the region’s initial mass function (IMF), particularly at the lowest masses (Section 7).

2. Catalog of Known Members of Taurus

For our census of Taurus, we begin with the 438 objects adopted as members by Luhman (2018), which were vetted for contaminants using the proper motions and parallaxes from Gaia DR2. In that catalog, the components of a given multiple system appeared as a single entry if they were unresolved by Gaia and the imaging data utilized by Esplin & Luhman (2017). Luhman (2018) overlooked the fact that HK Tau B and V1195 Tau B were resolved from their primaries by Gaia. They are now given separate entries in our census. We also adopt 2MASS J04282999+2358482 as a member, which was discovered to be a young late-M object by Gizis et al. (1999). It satisfies our photometric and astrometric criteria for membership and is located near other known members. We exclude from our membership list one of the stars from from Luhman (2018), 2MASS 05023985+2459337, for reasons discussed in the Appendix. When the 79 new members from our survey are included (Section 5), we arrive at a catalog of 519 known members of Taurus, which are presented in Table 1. That tabulation contains adopted spectral types, astrometry and photometry from Gaia DR2 and the corresponding kinematic populations from Luhman (2018), proper motions measured in Section 3.3, near-IR photometry from various sources, mid-IR photometry from Spitzer and WISE and the resulting disk classifications (Luhman et al., 2010; Esplin et al., 2014; Esplin & Luhman, 2017, Section 6), and extinction estimates. For each star that appears in Gaia DR2, we also list the value of the re-normalized unit weight error (RUWE, Lindegren, 2018), which indicates the quality of the astrometric fit (Section 4). Luhman (2018) compiled available radial velocity measurements for known members of Taurus and calculated $UVW$ velocities from the combination of those radial velocities and the Gaia proper motions and parallaxes. Two of the new members from our survey, Gaia 146708734143437568 and 152104381299305856, also have radial velocity measurements (16.6$\pm$0.8 km s*-1*, 17.5$\pm$1.6 km s*-1*), both of which are from Gaia DR2.

A map of the spatial distribution of the members is shown in Figure 1. Kinematic and photometric data for the members within nine fields that cover subsections of Taurus are plotted in Figures 2-10, which contain diagrams from Luhman (2018) that have been updated to include the new members from this work. The boundaries for those fields are indicated in Figure 1.

3. Identification of Candidate Members at Substellar Masses

3.1. Photometry and Astrometry

3.1.1 Data Utilized by Esplin & Luhman (2017)

In Esplin & Luhman (2017), we identified candidate substellar members of Taurus based on their proper motions and positions in color-magnitude diagrams (CMDs). We considered astrometry and photometry for objects within a field encompassing all of the Taurus clouds ($\alpha=4^{\rm h}$–$5^{\rm h}10^{\rm m}$, $\delta=15\arcdeg$–31$\arcdeg$) in several optical and IR bands: $JHK_{s}$ from the Point Source Catalog of the Two Micron All Sky Survey (2MASS, Cutri et al., 2003; Skrutskie et al., 2006), bands at 3.6, 4.5, 5.8, and 8.0 $\upmu$m ([3.6], [4.5], [5.8], [8.0]) from the Infrared Array Camera (IRAC; Fazio et al., 2004) on the Spitzer Space Telescope (Werner et al., 2004), $ZYJHK$ from data release 10 of UKIDSS, $rizy_{P1}$ from the first data release of PS1 (Chambers et al., 2016; Flewelling et al., 2016), $riz$ from data release 13 of the Sloan Digital Sky Survey (SDSS, York et al., 2000; Finkbeiner et al., 2004; Albareti et al., 2017), $G$ from the first data release of Gaia (Gaia Collaboration et al., 2016a, b), and bands at 3.5, 4.6, 12, and 22 $\upmu$m ($W1$, $W2$, $W3$, $W4$) from the AllWISE Source Catalog. The extinction for each object was estimated using $J-H$ and $J-K_{s}$ colors and it was used to deredden the photometry in the CMDs with reddening relations from Indebetouw et al. (2005), Schlafly et al. (2016), and Xue et al. (2016). We measured relative proper motions between 2MASS and Gaia DR1, between 2MASS and PS1, and across several epochs of IRAC imaging. Relative motions from UKIDSS were also employed. 2MASS, WISE, PS1 provided data for the entirety of our survey field while Spitzer, SDSS, and UKIDSS covered a subset of it (Luhman et al., 2017; Esplin & Luhman, 2017). The fields observed by IRAC are indicated in Figure 11.

3.1.2 UHS

New $J$-band photometry has become available in Taurus through the first data release of the UKIRT Hemisphere Survey (UHS, Dye et al., 2018). Those data were taken with UKIRT’s Wide Field Camera (WFCAM) (Casali et al., 2001), which also was used for UKIDSS. UHS provides $J$ photometry for a large portion of Taurus that was not observed by UKIDSS in that band. We have adopted the $1\arcsec$ aperture photometry from UHS, which has a similar completeness limit as the data from UKIDSS ($J\sim 18.5$).

3.1.3 UKIRT

UKIDSS has imaged most of Taurus in $K$ and roughly half of it in $ZYJ$. Only a small portion of Taurus was observed in $H$. When combined with $J$ and an optical band, $H$ is particularly useful for distinguishing late-type members from reddened background stars. To improve the coverage of Taurus in $H$ and the other bands, we have obtained new images with WFCAM at UKIRT. The observations were similar to those from UHS and UKIDSS, consisting of $3\times 15$ s exposures in $Y$ and $4\times 10$ s exposures in $JHK$ at each position. The data were collected between September and December of 2017. In Figure 11, we show the fields that now have $JHK$ photometry from WFCAM through UKIDSS, UHS, and our observations.

The initial data reduction steps (e.g., flat fielding, registration, coaddition) were performed by the WFCAM pipeline (Irwin et al., 2004; Hambly et al., 2008). We derived the flux calibration for the resulting images using photometry from previous surveys (e.g., PS1, 2MASS). The typical values of FWHM for point sources in the images were $1\farcs 1$ for $Y$ and $0\farcs 8$ for $JHK$. We identified sources in the pipeline images and measured aperture photometry for them using the routines starfind and phot in IRAF. We estimated the completeness limits of the data based on the magnitudes at which the logarithm of the number of stars as a function of magnitudes deviates from a linear slope and begins to decline, which were 18.5, 17.5, and 17.2 for $J$, $H$, and $K$, respectively. Similar limits are exhibited by the UKIDSS data in Taurus. Our $Y$ data have a completeness limit near 18.5, which is $\sim 0.5$ mag brighter than the value for UKIDSS.

3.1.4 CFHT

Near-IR images of portions of Taurus are publicly available from the archive of CFHT. We have utilized the data taken in $J$, $H$, and a narrowband filter at 1.45 $\upmu$m ($W$) with the Wide-field Infrared Camera (WIRCam) through programs 15BC11, 16AC13, 16BC17 (E. Artigau), 15BT11 (W.-P. Chen), 16AF16, 16BF22 (M. Bonnefoy), and 16AT04 (P. Chiang). For most of the observations, individual exposure times were 10, 10, and 65 s for $J$, $H$, and $W$, respectively, and the number of exposures per field was 4–8. Point sources in the images typically exhibited FWHM$\sim 0\farcs 6$–$0\farcs 8$. We began our analysis with the images from the CFHT archive that had been pipeline processed (e.g., flat fielding, dark subtraction, bad pixel masking). We registered and combined the images for a given field and filter. For the resulting mosaics, we derived the astrometric and flux calibrations with data from 2MASS and UKIDSS. Since $W$ is a custom filter that is absent from 2MASS and UKIDSS, we calibrated the relative photometry among different $W$ images such that their loci of reddened stars in $W-H$ versus $J-H$ were aligned with each other. Relative photometry of this kind in $W$ is sufficient for our purposes of identifying late-type objects based on colors. We identified sources in the images and measured their aperture photometry with starfind and phot in IRAF. The completeness limits for these data are $J=18.2$, $W=18.0$, and $H=17.5$. The fields covered by WIRCam are indicated in Figure 11.

3.2. Color-Magnitude Diagrams

We have identified all matching sources among our new catalogs and those considered by Esplin & Luhman (2017). When multiple measurements in similar bands were available for a star, we selected the data to adopt in the manner described by Esplin & Luhman (2017). We omitted photometry with errors $>0.15$ mag in $Y$ and $>0.1$ mag in the other bands. In Esplin & Luhman (2017), we constructed diagrams of $K_{s}$ (or $K$) versus $G-K_{s}$, $r-K_{s}$, $i-K_{s}$, $z_{\rm P1}-K_{s}$, $Z-K_{s}$, $y_{\rm P1}-K_{s}$, $Y-K_{s}$, $H-K_{s}$, $K_{s}-[3.6]$, and $K_{s}-W1$. We also included a diagram of $W1$ versus $W1-W2$. As explained in that study, we estimated the extinction for individual stars from $J-H$ and $J-K_{s}$ and dereddened the photometry in most of the CMDs. In each CMD, we marked a boundary that followed the lower envelope of the sequence of known members. Objects appearing above any of those boundaries and not appearing below any of them were treated as candidate members. We have applied those CMDs to our updated compilation of photometry. Four examples of the CMDs are presented in Figure 12. In addition, we show a diagram that makes use of the $W$-band data from WIRCam, $W-H$ versus $J-W$. The $W$ filter falls within a steam absorption band while $J$ and $H$ encompass continuum on either side of the band, so the combination of $J-W$ and $W-H$ can be used to identify late-type objects via their strong steam absorption. In the diagram of those colors, we have plotted a reddening vector near the lower edge of the population of known members later than M6. Objects above that vector are treated as late-type candidates as long as they are not rejected by any other diagrams. We note that many of the known $<$M6 members of Taurus within the WIRcam images are saturated, and hence are absent from the diagram of $W-H$ versus $J-W$.

3.3. Proper Motions

As mentioned in Section 3.1.1, Esplin & Luhman (2017) measured proper motions in Taurus with astrometry from 2MASS, PS1, Gaia DR1, and IRAC. In addition to those data, we have made use of new motions measured from a combination of 2MASS, IRAC, UKIDSS, UHS, and our new WFCAM data, which have epochs spanning 20 years. The latter four sets of data, which are deeper than 2MASS, span 13 years and reach the lowest masses in Taurus among the available motions. To measure the proper motions, we began by aligning each set of astrometry to the Gaia DR2 reference frame. Motions were then computed with a linear fit to the available astrometry. In Figure 13, we show the resulting motions for individual known members of Taurus and for other sources projected against Taurus, which are represented by density contours. The measurements for the known members have typical errors of $\sim 2$–3 mas yr*-1*. Motions with errors of $>10$ mas yr*-1* are ignored. As done with the other catalogs of proper motions in Esplin & Luhman (2017), we have identified candidate members based on motions that have 1$\sigma$ errors overlapping with a radius of 10 mas yr*-1* from the median motion of the known members (Figure 13). Six known members of Taurus do not satisfy this threshold, three of which have Gaia DR2 motions that are consistent with membership (Luhman, 2018). The remaining three sources are 2MASS J04355209+2255039, J04354526+2737130, and J04574903+3015195. The first two objects also have discrepant motions in Gaia DR2, but are retained as members for reasons discussed by Luhman (2018). The third star is retained as a member since it is near known members and is only slightly beyond our proper motion threshold.

4. Identification of Candidate Members at Stellar Masses

Gaia DR2 provides high-precision astrometry at an unprecedented depth for a wide-field survey. For stars at $G\lesssim 20$, the Gaia parallaxes and proper motions have typical errors of $\lesssim 0.7$ mas and $\lesssim 1.2$ mas yr*-1*, respectively (Gaia Collaboration et al., 2018), which correspond to errors of $\lesssim 10$% and $\lesssim 5$%, respectively, for unreddened members of Taurus at masses of $\gtrsim 0.05$ $M_{\odot}$. As a result, Gaia DR2 enables the precise kinematic identification of members of Taurus at stellar masses.

Luhman (2018) selected stars from Gaia DR2 that have proper motions and parallaxes that are similar to those of the known members of Taurus. In that analysis, the parameters astrometric_gof_al and astrometric_excess_noise from Gaia DR2 were used to identify stars with poor astrometric fits, and hence potentially unreliable astrometry. More recently, Lindegren (2018) has presented a new parameter, RUWE, that serves as a better indicator of the goodness of fit. He found that the distribution of RUWE in Gaia DR2 exhibited a break near 1.4 between the distribution centered at unity expected for well-behaved fits and a long tail to higher values. Thus, RUWE$\lesssim$1.4 could be adopted as a criterion for reliable astrometry. To illustrate the application of this threshold to Taurus, we plot in Figure 14 the distribution of log(RUWE) for known members (including the new ones from this work) that have parallaxes and proper motions from Gaia DR2. We also indicate the subset of members that are noted in Luhman (2018) and the Appendix as having discrepant parallaxes (Table 1). The latter distribution does begin just above the threshold of 1.4 from Lindegren (2018), supporting its applicability to Taurus. Above that threshold, the fraction of members with discrepant astrometry increases with higher values of RUWE. Most members with RUWE$>1.4$ do not have discrepant astrometry, indicating that many stars with high RUWE have fits that are sufficiently good for useful astrometry.

The selection criteria from Luhman (2018) produced a sample of 62 candidate members of Taurus. Most of the candidates should have spectral types of M2–M6 based on their colors. In the next section, we present spectroscopic classifications for 61 of those stars, 54 of which are adopted as members. The one remaining candidate that lacks a spectrum is Gaia 157816859599833472. It is located $6\arcsec$ from a much brighter star, HD 30111. The two stars have similar proper motions, but the parallax of HD 30111 ($3.0\pm 0.2$ mas) is much smaller than those of Taurus members (6–8 mas), so it was not selected as a candidate member. However, the value of RUWE for HD 30111 is high enough (2.4) to indicate a poor astrometric fit and potentially unreliable astrometry. Therefore, based on its proximity to the candidate Gaia 157816859599833472 and its similar motion, we treat HD 30111 as a candidate member.

Luhman (2018) noted three stars that did not satisfy the selection criteria for candidates but were located within a few arcseconds of candidates, and hence could be companions to them. They consist of Gaia 164475467659453056, Gaia 3314526695839460352, and Gaia 3409647203400743552. We present spectral classifications for those stars in the next section.

We have searched for additional companions that were detected by Gaia but were not identified as candidate members by Luhman (2018). We began by retrieving all sources from Gaia DR2 that are within $5\arcsec$ from known Taurus members. We omitted companions or candidate companions that were already known and stars that appear below the sequence of Taurus members in CMDs of Gaia photometry. The remaining sample consists of Gaia 152416436441091584, Gaia 3415706130945884416, Gaia 148400225409163776, and Gaia 154586322638884992. All of these stars have photometry in only one Gaia band. The first two objects lack measurements of proper motion and parallax. Those parameters have large uncertainties for 148400225409163776, but are similar to the measurements for its primary. The proper motions and parallaxes of 154586322638884992 and its primary differ significantly, but the latter may have unreliable astrometry based on the large value of its RUWE (7.2).

The six candidates discussed in this section that lack spectroscopy are listed in Table 2.

5. Spectroscopy of Candidate Members

5.1. Observations

We have obtained spectra of 140 candidate members of Taurus identified in Sections 3 and 4111Three of these candidates were found independently by Zhang et al. (2018) and are treated as previously known members in this work., three known companions that lack spectral classifications, and the primary for one of the latter stars. We also searched for publicly available spectra of our candidates in the data archives of observatories and spectroscopic surveys, finding spectra with sufficient signal-to-noise ratios (SNRs) for 38 objects. Those archival observations consist of 31 optical spectra from the third data release of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope survey (LAMOST; Cui et al., 2012; Zhao et al., 2012) and seven IR spectra collected through programs GN-2017A-Q-81, GN-2017B-Q-35 (L. Albert), and GN-2017B-Q-19 (E. Magnier) with the Gemini Near-Infrared Spectrograph (GNIRS; Elias et al., 2006). We present spectra for a total of 168 objects, some of which were observed with multiple instruments. This spectroscopic sample includes 61 of the 62 candidates identified by Luhman (2018), three additional stars from that study that did not satisfy the criteria for candidacy but were located very close to candidates (see Section 4), three known companions in Taurus that lack measured spectral types (JH223 B, XEST 20-071 B, V892 Tau NE), and XEST 20-071 A, which was observed at the same time as its companion. The remaining 100 targets in our sample were selected from the candidates identified in Section 3. The highest priority was given to candidates within the area of full $JHK$ coverage from WFCAM (Figure 11).

We performed our spectroscopy with the Red Channel Spectrograph (Schmidt et al., 1989) and the MMT and Magellan Infrared Spectrograph (MMIRS; McLeod et al., 2012) at the MMT, GNIRS and the Gemini Multi-Object Spectrograph (GMOS; Hook et al., 2004) at Gemini North, SpeX (Rayner et al., 2003) at the NASA Infrared Telescope Facility (IRTF), and the Low-Resolution Spectrograph 2 (LRS2; Chonis et al., 2014, 2016) at the Hobby-Eberly Telescope (HET). The instrument configurations are summarized in Table 3. The date and instrument for each object are listed in Table 4. The archival data from LAMOST and GNIRS have been included in Tables 3 and 4.

We reduced the data from SpeX with the Spextool package (Cushing et al., 2004) and corrected them for telluric absorption using spectra of A0V stars (Vacca et al., 2003). The GNIRS and MMIRS data were reduced and corrected for telluric absorption in a similar manner using routines within IRAF. The optical spectra from the Red Channel and GMOS were also reduced with IRAF. The LRS2 data were processed with the LRS2 Quick-Look Pipeline (B. L. Indahl, in preparation), which is briefly described by Davis et al. (2018). Fully reduced spectra are provided by the LAMOST survey. We present examples of the reduced optical and IR spectra in Figures 15 and 16, respectively. All of the reduced spectra are provided in electronic files that accompany those figures with the exception of the LAMOST data, which are available from http://www.lamost.org.

5.2. Spectral Classification

We have used the spectra from the previous section to estimate spectral types and to identify evidence of youth that would support membership in Taurus. Given their colors and magnitudes, the candidates in our spectroscopic sample should have M/L spectral types if they are members. For these types, we have utilized diagnostics of youth that include Li I absorption at 6707 Å and gravity-sensitive features like the Na I doublet near 8190 Å and the shape of the $H$-band continuum (Martín et al., 1996; Luhman et al., 1997; Lucas et al., 2001). Our measurements of the equivalent widths of Li I are listed in Table 4 and are plotted versus spectral type in Figure 17. For the range of spectral types of the objects with useful Li constraints ($\geq$K7), most known members of Taurus have equivalent widths of $\gtrsim$0.4 Å (Basri et al., 1991; Magazzú et al., 1992; Martín et al., 1994). For young objects at $<$M5 and field dwarfs, we classified the optical spectra through comparison to dwarf standards (Kirkpatrick et al., 1991, 1997; Henry et al., 1994). The optical data for young sources at $\geq$M5 were classified with the average spectra of dwarf and giant standards (Luhman et al., 1997; Luhman, 1999). For the near-IR spectra, we applied young standards (Luhman et al., 2017) and dwarf standards (Cushing et al., 2005; Rayner et al., 2009) as appropriate. The resulting classifications are listed in Table 4. For the young objects that were observed with IR spectroscopy, we have used the slopes of those data relative to the best-fitting standards to derive estimates of extinction. Spectra of young L dwarfs with low-to-moderate SNRs can be matched by standards across a wide range of types when extinction is a free parameter (Luhman et al., 2017), as illustrated in Figure 16, where three of the coolest new members are compared to standard spectra bracketing their classifications.

Moderately young stars ($\sim$10–100 Myr) that are unrelated to the Taurus clouds ($\sim 2$ Myr, Palla & Stahler, 2000) are scattered across the large field that we have selected for our survey (Luhman, 2018, references therein). As a result, a spectroscopic signature of youth may not be sufficient evidence of membership in Taurus, particularly if it provides only a rough constraint on age (e.g., $<100$ Myr). In addition, some of the young contaminants have proper motions that are close enough to those of Taurus members that the former can appear to have motions consistent with membership when the errors are $\gtrsim 3$ mas yr*-1*, which applies to most non-Gaia data (Luhman, 2018). Given these considerations, we have taken the following approach to assigning membership in our spectroscopic sample. We treat an object as a member if its proper motion and parallax from Gaia DR2 support membership (i.e., the candidates from Luhman (2018)) and its spectrum shows evidence of youth, which is taken to be $W_{\lambda}\gtrsim 0.4$ Å when a Li measurement is available. If Li is detected at a weaker level ($\gtrsim$0.15 Å) and the Gaia data agree closely with those of known members, we also adopt the star as a member (Appendix). Candidate companions to known members are adopted as members if they have spectroscopic signatures of youth. Discrepant Gaia astrometry is ignored when the astrometric fit is poor (RUWE$\gtrsim 1.4$), which applies to some of the candidate companions. If Gaia does not offer reliable measurements of parallax and proper motion, a candidate is adopted as a member if its available proper motion data are consistent with membership, its spectrum shows evidence of youth, it appears within the sequence of known members in CMDs and in a diagram of $M_{K}$ versus spectral type, and it is within $\sim 1\arcdeg$ of known members.

Based on the above criteria, 86 of the 168 objects in our spectroscopic sample are members of Taurus, as indicated in Table 4. Three members were previously known companions that lacked spectral classifications, one member is the primary for one of those companions, and three members were independently found in a recent survey (Zhang et al., 2018). The remaining 79 members are newly confirmed in this work. As discussed in Section 2, the census of Taurus now contains 519 known members. Our survey has doubled the number of known members at $\geq$M9 and has uncovered the faintest known members in $M_{K}$, as illustrated in Figure 18, where we show extinction-corrected $M_{K}$ versus spectral type for previously known members and our new members. UGCS J041757.97+283233.9 is now the faintest known member. It has a very red spectrum, which is consistent with spectral types ranging from M9 ($A_{V}=7.6$) to L7 ($A_{V}=0$), as illustrated in Figure 16. Assuming a $K$-band bolometric correction for young L dwarfs (Filippazzo et al., 2015), the median parallax of 7.8 mas for the nearest group of members, and $A_{V}=3.5$, we estimate log $L_{\rm bol}=-3.76$ for UGCS J041757.97+283233.9, which implies a mass of 0.003–0.01 $M_{\odot}$ ($\sim$3–10 $M_{\rm Jup}$) for ages of 1–10 Myr according to evolutionary models (Burrows et al., 1997; Chabrier et al., 2000).

Most (54/61) of the candidate members identified with Gaia data by Luhman (2018) have been adopted as Taurus members. Among the other candidates that were not part of that sample, 39 are field stars that were observed prior to our WFCAM imaging and the release of Gaia DR2 and that would be rejected by our current criteria that incorporate those data.

Luhman (2018) found that members of Taurus exhibit four distinct populations in terms of parallax and proper motion, which were given names of red, blue, green, and cyan. We have assigned the new members to those populations when the necessary data are available from Gaia DR2, as indicated in Table 1 and Figures 2–10.

Comments on the spectral types, membership, and kinematics of individual objects are provided in the Appendix.

6. Circumstellar Disks

6.1. Disk Detection and Classification

We have compiled the available mid-IR photometry of the new members of Taurus from this work to check for evidence of circumstellar disks via the presence of IR emission in excess above the expected photospheric emission. We also have performed this analysis on members adopted by Luhman (2018) that were not examined for disks by Esplin & Luhman (2017) or earlier studies. We make use of photometry in $W1$–$W4$ from the AllWISE Source Catalog, [3.6]–[8.0] from IRAC on Spitzer, and the 24 $\upmu$m band of the Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al., 2004), which is denoted as [24]. The Spitzer data were measured in the manner described by Luhman et al. (2010). We present the resulting WISE and Spitzer data in Table 1. In addition, we have included photometry from those facilities for previously known members (Luhman et al., 2010; Esplin et al., 2014; Esplin & Luhman, 2017).

To determine if excess mid-IR emission is present in a given object and to classify the evolutionary stage of a detected disk, we have followed the methods and terminology described in Luhman et al. (2010) and Esplin et al. (2014) (see also Esplin et al., 2018). In summary, we calculated extinction-corrected colors of the mid-IR photometry relative to $K_{s}$, measured color excesses relative to photospheric colors, and used the sizes of those excesses (when present) to estimate the evolutionary stages of the disks. The colors utilized for that analysis are plotted as a function of spectral type in Figure 19 for both previously known members and the newly classified members. The disks are assigned to the following categories: optically thick full (primordial) disks with no large gaps or holes that affect the mid-IR spectral energy distribution (SED); optically thick transitional disks with large inner holes; optically thin evolved disks with no large gaps; optically thin evolved transitional disks with large inner holes; and optically thin debris disks that are composed of second-generational dust from planetesimal collisions (Kenyon & Bromley, 2005; Rieke et al., 2005; Hernández et al., 2007; Luhman et al., 2010; Espaillat et al., 2012).

The Taurus members that have been found since Esplin & Luhman (2017) are plotted with red and blue symbols in Figure 19 according to the presence or absence of excess emission, respectively. Ten of those stars exhibit mid-IR excess emission. Four of them have excesses only in [24] or $W4$, although one of them, HD 30378 (B9.5), is only slightly below our adopted excess threshold in $W3$. The excesses are small ($\sim 0.5$ mag) for the other three stars with excesses in only [24]/$W4$, which consist of 2MASS J04355694+2351472 (M5.75), 2MASS J04390571+2338112 (M6), and 2MASS J04584681+2954407 (M4). Two M9.5 members, 2MASS J04213847+2754146 and UGCS J042438.53+264118.5, have excesses in $[4.5]$, $W2$, and [8.0] and lack reliable detections at longer wavelengths. 2MASS J04451654+3141202 (M5.5) has excesses in $W2$ and $W3$. It is blended with another source in the ${\it WISE}$ images, but it clearly dominates in $W3$. 2MASS 04282999+2358482 (M9.25) and UGCS J043907.76+264236.0 (M9.5–L4) have marginal excesses at [8.0] and UGCS J041757.97+283233.9 (M9-L7) has a marginal excess at [4.5]. The latter is the faintest known member in extinction-corrected $K$. It is difficult to reliably identify the presence of excess emission for the coolest members because of the uncertainties in the photospheric colors and the spectral classifications of young L-type objects (Esplin & Luhman, 2017; Esplin et al., 2017). The evolutionary stages assigned to the newly identified disks are presented in Table 1, where we also include the classifications of previously known members (Luhman et al., 2010; Esplin et al., 2014; Esplin & Luhman, 2017).

6.2. Disk Fraction

Luhman et al. (2010) measured the fraction of Taurus members that have disks as a function of spectral type (and hence mass) for known members observed by Spitzer. Since that study, mid-IR photometry has become available for additional members from both Spitzer and WISE and many new members have been identified. Therefore, it would be worthwhile to perform a new calculation of the disk fraction in Taurus using our new catalog of members.

The evolutionary stages of young stellar objects consist of classes 0 and I (protostar+disk+infalling envelope), class II (star+disk), and class III (star without disk; Lada & Wilking, 1984; Lada, 1987; André et al., 1993; Greene et al., 1994). Taurus members that have been previously designated as class 0 or class I are marked as such in Table 1. We consider all other members with disks to be class II objects. Some disks have classifications of “debris/evolved transitional” because we cannot distinguish between these two classes with the available data. Stars with debris disks are normally counted as class III objects, but since very few debris disks are expected in a region as young as Taurus, we treat all of the “debris/evolved transitional” disks as class II.

As done in Luhman et al. (2010), we define the disk fraction as N(II)/N(II+III) and we measure it as a function of spectral type using bins of $<$K6, K6–M3.5, M3.75–M5.75, M6–M8, and M8–M9.75. We exclude stars that lack measured spectral types, all of which are protostars or close companions. We also omit objects with spectral types of $\geq$L0 because of the difficulty in reliably identifying the presence of excess emission from disks (Section 6.1). The resulting disk fraction is tabulated and plotted in Table 5 and Figure 20, respectively.

The current census of class II members of Taurus should have a high level of completeness for spectral types earlier than $\sim$M8 (Esplin et al., 2014). However, the census may be incomplete for class III at high extinctions, which would lead to an overestimate of the disk fraction when all known members are considered. To investigate this possibility, we have computed disk fractions for samples of members that should be complete for both classes II and III. Now that most of the candidate members identified with Gaia by Luhman (2018) have been observed spectroscopically, the census should be complete for both class II and class III members earlier than M6–M7 at low extinctions ($A_{J}<1$, Luhman, 2018). Meanwhile, the census within the WFCAM field in Figure 11 should be complete for $\lesssim$L0 at $A_{J}<1.5$ (Section 7.1). We find that the disk fractions for $A_{J}<1$ across the entirety of Taurus and for $A_{J}<1.5$ within the WFCAM fields are indistinguishable from the disk fraction in Figure 20 for all known members.

The disk fraction in Figure 20 is near $\sim 0.7$ and 0.4 for spectral types of $\leq$M3.5 and $>$M3.5, respectively. A similar trend with spectral type was present in the data from Luhman et al. (2010), although the disk fraction was slightly higher than our new measurement ($\sim 0.75$ and 0.45). The disk fraction in Taurus is similar to that in Chamaeleon I, which is $\sim$0.7 and 0.45 for $\leq$M3.5 and $>$M3.5 (Luhman et al., 2010). For all spectral types combined, Taurus has a disk fraction of $\sim$0.5, which is roughly similar to the disk fractions of IC 348 and NGC 1333 ($\sim$0.4 and 0.6). However, those two clusters do not show a variation with spectral type (Luhman et al., 2016).

7. Initial Mass Function

7.1. Completeness

To derive constraints on the IMF in Taurus from our new census of members, we begin by evaluating the completeness of that census.

In Section 3, we focused on the identification of candidate substellar members within the WFCAM fields in Figure 11. To evaluate the completeness of our census within that field, we employ a CMD constructed from $H$ and $K_{s}$, which offer the greatest sensitivity to low-mass members of Taurus among the available bands. In Figure 21, we plot $K_{s}$ versus $H-K_{s}$ for the known members in the WFCAM fields and all other sources in those fields that 1) are not rejected by the photometric and proper motion criteria from Section 3 or the astrometric criteria from Luhman (2018) and 2) are not known nonmembers based on spectroscopy or other data. There are very few remaining sources with undetermined membership status within a wide range of magnitudes and reddenings. For instance, the current census within the WFCAM fields should be complete for an extinction-corrected magnitude of $K_{s}<15.7$ ($\lesssim$L0) for $A_{J}<1.5$.

In Section 4, we adopted the candidate stellar members that were identified by Luhman (2018) using data for the entirety of Taurus from Gaia DR2. That study demonstrated that the census of Taurus should be complete for spectral types earlier than M6–M7 at $A_{J}<1$ after including the Gaia candidates that are spectroscopically confirmed to be members.

7.2. Distributions of Spectral Type, $M_{K}$, and Mass

Based on the analysis in the previous section, we have defined two extinction-limited samples of known Taurus members that should have well-defined completeness limits, making them suitable for characterizing the IMF: members in the WFCAM fields with $A_{J}<1.5$ and members at any location with $A_{J}<1$. Stars that lack extinction estimates are excluded from these samples, which consist of protostars, close companions, and edge-on disks. As done in our recent studies of IC 348, NGC 1333, and Chamaeleon I (Luhman et al., 2016; Esplin et al., 2017), we use distributions of spectral types and extinction-corrected $M_{K}$ as observational proxies for the IMF. The distributions of these parameters for our two extinction-limited samples are presented in Figure 22. For objects that lack parallax measurements, we derived $M_{K}$ using the median parallax of the nearest population of members. In addition, we have estimated the IMF for each sample using distributions of spectral types in which the bins are selected to approximate logarithmic intervals of mass according to evolutionary models (Baraffe et al., 1998, 2015) and the temperature scale for young stars (Luhman et al., 2003), as done for the disk fraction in Figure 20. The resulting IMFs are shown in Figure 22.

The two samples of Taurus members in Figure 22 have similar distributions, which is not surprising given the large overlap between the fields in question (i.e., the WFCAM fields encompass a large majority of known members). Luhman (2018) found that a $A_{J}<1$ sample of members with the Gaia candidates included exhibited a prominent maximum at M5 ($\sim 0.15$ $M_{\odot}$), and thus resembled denser clusters like IC 348, NGC 1333, Chamaeleon I, and the Orion Nebula Cluster (Da Rio et al., 2012; Hillenbrand et al., 2013; Luhman et al., 2016; Esplin et al., 2017). Since we have confirmed most of the Gaia candidates as members, our $A_{J}<1$ sample in Figure 22 has a similar distribution of spectral types as in Luhman (2018).

In the $A_{J}<1.5$ sample for the WFCAM fields, the distributions of spectral type and $M_{K}$ decrease rapidly below the peak and remain roughly flat at substellar masses down to the completeness limit, which corresponds to $\sim 5$–13 $M_{\rm Jup}$ for ages of 1–10 Myr according to evolutionary models (Burrows et al., 1997; Chabrier et al., 2000). Thus, our completeness limit in that sample does not appear to be near a low-mass cutoff. The faintest known member, UGCS J041757.97+283233.9, has an estimated mass of $\sim$3–10 $M_{\rm Jup}$ (Section 5.2), which represents an upper limit on the minimum mass in Taurus. These results are consistent with recent surveys for brown dwarfs in other star-forming regions (Luhman et al., 2016; Esplin & Luhman, 2017; Zapatero Osorio et al., 2017; Lodieu et al., 2018), young associations (Liu et al., 2013; Kellogg et al., 2015; Schneider et al., 2016; Best et al., 2017), and the solar neighborhood (Kirkpatrick et al., 2019), which have found that the IMF extends down to $\lesssim 5$ $M_{\rm Jup}$. Using the minimum variance unbiased estimator for a power-law distribution, we calculate a slope of $\alpha=1.0\pm 0.1$222$\alpha$ is defined such that $dN/dM\propto M^{-\alpha}$. $\alpha=1$ corresponds to a slope of zero when the mass function is plotted in logarithmic units, as done in Figure 22. between the hydrogen burning limit and the completeness limit (0.01–0.08 $M_{\odot}$) in the IMF for the $A_{J}<1.5$ sample, which is shallower than the slope of $\alpha\sim-0.3$ in the lognormal mass function from Chabrier et al. (2005).

8. Conclusion

In Esplin & Luhman (2017), we searched for substellar members of Taurus using photometry and proper motions from 2MASS, UKIDSS, PS1, SDSS, Spitzer, WISE, and Gaia DR1. We have identified additional candidate members by incorporating new data from UKIRT and CFHT. In Luhman (2018), candidate members at stellar masses were identified with high-precision proper motions and parallaxes from Gaia DR2. We have measured spectral types and assessed membership for candidates from these two samples using optical and IR spectra. Through this analysis, we have identified 79 new members of Taurus, which brings the total number of known members in our census to 519. Our survey has doubled the number of known members at $\geq$M9 and has uncovered the faintest known members in $M_{K}$, which should have masses extending down to $\sim 3$–10 $M_{\rm Jup}$ for ages of 1–10 Myr (Burrows et al., 1997; Chabrier et al., 2000).

According to data from Gaia DR2, our census of Taurus should be nearly complete for spectral types earlier than M6–M7 at $A_{J}<1$ across the entire cloud complex (Luhman, 2018). Meanwhile, we have demonstrated that the census should be complete for extinction-corrected magnitudes of $K<15.7$ at $A_{J}<1.5$ within a large field that encompasses $\sim 72$% of the known members. That magnitude limit corresponds to $\sim 5$–13 $M_{\rm Jup}$ for ages of 1–10 Myr. For the known members within that field and extinction limit, we have used distributions of spectral types and $M_{K}$ as observational proxies for the IMF. Those distributions remain roughly constant at substellar masses down to the completeness limit, and thus show no sign of a decline towards a low-mass cutoff.

We have used mid-IR photometry from Spitzer and WISE to search for evidence of circumstellar disks among the new members from our survey, as well as the few members adopted by Luhman (2018) that were not examined for disks by Esplin & Luhman (2017) or earlier studies. By combining those results with disk classifications for all other members in our census (Luhman et al., 2010; Esplin et al., 2014; Esplin & Luhman, 2017), we have derived a disk fraction of $\sim$0.7 and 0.4 for spectral types of $\leq$M3.5 and $>$M3.5, respectively, which is slightly lower than previous measurements based on less complete catalogs of members (Luhman et al., 2010).

K.L. acknowledges support from NASA grant 80NSSC18K0444. The UKIRT data were obtained through program U/17B/UA05. UKIRT is owned by the University of Hawaii (UH) and operated by the UH Institute for Astronomy. When the data reported here were acquired, UKIRT was supported by NASA and operated under an agreement among the University of Hawaii, the University of Arizona, and Lockheed Martin Advanced Technology Center; operations were enabled through the cooperation of the East Asian Observatory. The Gemini data were obtained through programs GN-2017B-Q-8, GN-2018B-Q-114, GN-2018B-FT-205, GN-2018B-FT-207. Gemini is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil). The IRTF is operated by the University of Hawaii under contract NNH14CK55B with NASA. The MMT Observatory is a joint facility of the University of Arizona and the Smithsonian Institution. LRS2 was developed and funded by the University of Texas at Austin McDonald Observatory and Department of Astronomy and by Pennsylvania State University. We thank the Leibniz-Institut für Astrophysik Potsdam (AIP) and the Institut fur Astrophysik Göttingen (IAG) for their contributions to the construction of the integral field units. The HET is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximillians-Universität München, and Georg-August-Universität Göttingen and is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The LAMOST data were obtained with the Guoshoujing Telescope, which is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. WIRCAM is a joint project of CFHT, Taiwan, Korea, Canada, France, and the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. The Spitzer Space Telescope and the IPAC Infrared Science Archive (IRSA) are operated by JPL and Caltech under contract with NASA. 2MASS is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center (IPAC) at Caltech, funded by NASA and the NSF. Funding for SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the NSF, the U.S. Department of Energy, NASA, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, The University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy, the Max-Planck-Institute for Astrophysics, New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. PS1 and its public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the NSF Grant AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. *Facilities: * UKIRT (WFCAM), MMT (Red Channel, MMIRS), Gemini:North (GMOS, GNIRS), CFHT (WIRCam), IRTF (SpeX), Spitzer (IRAC), HET (LRS2)

Appendix A Comments on Individual Sources

Gaia 164475467659453056 and 164475467657712256 (2MASS J04161407+2758275 N and S) comprise a pair with a separation of $0\farcs 9$ (Section 4). The first component has a discrepant parallax for Taurus membership (Figure 2), but its astrometry is probably unreliable based on its large RUWE (5.1) and the Gaia data for the second component, which support membership. LAMOST provides a spectrum of the combined light from the pair. Since the components have similar $G$ magnitudes, we have assigned the resulting spectral classification to both of them. In the diagram of $M_{J}$ versus spectral type in Figure 2, only the second component is plotted, and that is done using half of the $J$-band flux from 2MASS.

2MASS J04053214+2733139, 2MASS J04064263+2902014, 2MASS J04212650+2952476, and 2MASS J04422776+2939448 are not within any of the fields marked in Figure 1 and shown in Figures 2–10. The data for those stars are included in the photometric and kinematic diagrams of neighboring fields, corresponding to Figures 2, 2, 3, and 9, respectively.

2MASS J04334298+2235566 is intermediate between the red and blue populations in terms of parallax (Figure 6). We have assigned it to the red group based on better agreement in proper motion.

The parallax and proper motion of 2MASS J04343664+1836255 are inconsistent with membership, but those data are probably unreliable (RUWE=8.2). In Figure 8, the star is beyond the boundaries of the parallax diagram, labeled in the proper motion diagram, and omitted from $M_{J}$ versus spectral type.

The previously known members 2MASS J05080816+2427150 A and B comprise a $0\farcs 94$ pair. The former lacks measurements of proper motion and parallax from Gaia, likely due to a poor astrometric fit (RUWE=71). The secondary has a discrepant proper motion (Figure 10), which is probably unreliable (RUWE=3.0).

As mentioned in Section 2, we have adopted 2MASS J04282999+2358482 as a Taurus member, which was classified as a young M8 dwarf by Gizis et al. (1999). Using our classification methods, we have measured a spectral type of M9.25 from the optical spectrum in that study.

Because of its moderately low SNR, the spectrum of UGCS J042443.77+270453.4 can be matched with either a young early-L dwarf or an old mid-L dwarf. We measure a proper motion of ($\mu_{\alpha},\mu_{\delta}=2.9\pm 1.3,-16.8\pm 5.3$ mas yr*-1*) from the data in Section 3.3, which is consistent with membership (Figure 13). Its small distance from a known member ($3\arcmin$) is also suggestive of membership. We tentatively adopt it as a member, but a spectrum with higher SNR would be useful for confirming its youth.

2MASS J04575235+2954072 exhibits evidence of youth in the form of Li absorption, but the feature is weaker than in most K/M Taurus members (0.2 Å vs. $\gtrsim 0.4$ Å). The star agrees well with its neighboring known members in terms of parallax, proper motion, and the age implied by $M_{J}$ versus spectral type, so we adopt it as a member.

The LAMOST spectrum of 2MASS J04053214+2733139 shows Li absorption (0.4 Å) while the resolution of the spectrum from Red Channel is too low for a useful constraint on the feature. The star’s parallax and proper motion closely match those of the red group in Figure 2, but given the large distance from that group ($\sim 2\arcdeg$), we consider its membership to be tentative.

2MASS J04404677+1928033 and 2MASS J05080636+3026233 have moderately weak Li (0.3 Å) for Taurus members and share similar kinematics as the blue and cyan groups in Figures 8 and 9, respectively. We adopt both stars as members, but the membership of the former is considered tentative because of its large distance from other members.

2MASS J04474012+2850409, 2MASS J04491437+2934354, and 2MASS J04505864+2852218 are among the Gaia candidates from Luhman (2018) and are located near each other in the field in Figure 9, where they are plotted as crosses. The second star has Li absorption comparable to that of Taurus members (0.48 Å) while the other stars have unusually weak Li for Taurus (0.18 Å). The three stars exhibit nearly identical parallaxes, proper motion offsets, and ages (Figure 9), indicating that they are members of a coeval, comoving group. The weak Li lines for two of the stars are consistent with the ages implied by the diagram of $M_{J}$ versus spectral type (10–20 Myr). Their parallaxes and motions are distinct from those of the Taurus populations, so we classify them as nonmembers. We note that a few of the known members in Figure 9 have proper motion offsets that appear to be as discrepant as those of the three stars in the preceding discussion (e.g., the stars at the top and bottom of the clump of members). All of those outliers have RUWE$\gtrsim$1.4, so their discrepant offsets may be due to poor astrometric fits.

2MASS J04404936+2732166 is plotted as the cyan open square in Figure 5. In terms of parallax and proper motion offset, it matches more closely with the cyan population in the neighboring field in Figure 9 than the red population in Figure 5, although there remains a modest difference in proper motion offsets. Its gravity-sensitive spectral features and position in the diagram of $M_{J}$ versus spectral type are consistent with the age of that cyan population, so we tentatively assign membership to it.

2MASS J04292852+2106069 is located between the fields for Figures 6 and 8. The presence of Li absorption indicates youth. Although it was identified as a candidate member based on its parallax and proper motion (Luhman, 2018), it is near the thresholds for selection in both parameters. Given its remote location and modest discrepancy in parallax and proper motion relative to other members, we treat its membership as undetermined.

2MASS J04443916+2224417 shows evidence of moderate youth in its weak Li absorption (0.15 Å), but it does not agree well with any of the groups of known members in terms of its parallax and proper motion, so we classify it as a nonmember.

2MASS J05023985+2459337 and 2MASS J05010116+2501413 are marked with crosses in Figure 10. Luhman (2018) adopted the former as a member of Taurus, but noted that it exhibits a discrepant proper motion offset relative to Taurus members in its field. The second star was selected by Luhman (2018) as a candidate member using Gaia astrometry, appearing near the threshold for selection in proper motion offset. The two stars have similar proper motion offsets, parallaxes, and ages (Figure 10), indicating that they are likely associated with each other. We classify them as nonmembers based on their discrepant motions relative to the Taurus members in their field.

2MASS J04195030+2926477 exhibits signatures of youth in its optical and near-IR spectra. Its Gaia astrometry is inconsistent with membership, but those data may not be reliable (RUWE=1.95). Given its remote location relative to the Taurus groups (slightly beyond the northern boundary of Figure 3), youth alone is insufficient evidence of membership, so we treat it as a nonmember.

Luhman (2018) noted that T Tau differs from the other members of its red population in terms of its proper motion offset (Figure 8). Its value of RUWE is somewhat high (1.7, Figure 14), so it may have a poor astrometric fit, which could explain this discrepancy.

In Section 5.1, we classified seven of our candidate members of Taurus using IR spectra that were publicly available from Gemini programs GN-2017A-Q-81, GN-2017B-Q-19, and GN-2017B-Q-35. Although they were not selected as candidates in our analysis, we have examined the spectra of the remaining 38 objects from those programs. One of the targets is a previously known member of Taurus, UGCS J043354.07+225119.1 (Esplin & Luhman, 2017). We classify one source as a galaxy and 34 sources as field stars. The remaining two objects, 2MASS J04390237+2332133 and UGCS 044344.10+261749.9, appear to be young and have spectral types of M9–L1 based on comparison to the young standards from Luhman et al. (2017). However, both of them fall below the sequence of known members in multiple CMDs. Young stars that are seen in scattered light can appear underluminous for their colors, but these two objects do not show evidence of circumstellar disks in their mid-IR photometry. Instead, they may be members of the populations of intermediate-age stars ($\gtrsim 10$ Myr) in the direction of Taurus that are unrelated to the cloud complex and its newly-formed stars (Luhman, 2018). We measure proper motions of $(10.6\pm 2.4,-29.0\pm 5.3$ mas yr*-1*) for 2MASS J04390237+2332133 and $(16.4\pm 7.4,-45.1\pm 2.9$ mas yr*-1*) for UGCS 044344.10+261749.9. The former is consistent with membership while the latter is not. Given its proper motion and proximity to known members, 2MASS J04390237+2332133 seems more likely to be a member, but we treat both objects as nonmembers based on their underluminous nature.